AP Calc

Find the zeros

Set function = 0, factor or use quadratic equation if

quadratic, graph to find zeros on calculator

find the interval where f(X) is increasing

Find f’(x) , set both numerator and denominator to

zero to find critical points, make sign chart of f’(x)

and determine where it is positive

Find equation of the line tangent to f(x) on [a,b]

Take derivative = f’(a) = m and use y-y1 = m(x-x1)

Find interval where the slope of f(x) is increasing

Find the derive of f’(x)=f’’(x) set both numerator and denominator zero to find critical points, make sign chart of f’’(x) and determine where it is positive

Find the minimum value of a function

Make a sign chart of f’(x) find all relative minimums and plug those values back into f(x) and choose the smallest

Find critical values

Express f’(x) as a fraction and set both numerator and denominator equal to zero

Find inflection points

Express f’’(x) as a fraction and set both numerator and denominator to zero. Make sign chart of f’’(x) to find where it changes sign

Show that lim (x→a) f(x) exists

Show that lim (x→a-) f(x) = lim (x→a+) f(x)

Show that f(x) is continuous

She that 1) lim x→a f(x) exists, 2) f(a) exists, 3) the two are equal

Find vertical asymptotes of f(x)

Do all factor/cancel of f(x) and set denominator= 0

Find of horizontal asymptotes of f(x)

Find lim x→infinitiy f(x) and lim x→-infinity f(x)

Find the average rate of change of f(x) on [a,b]

Find f(b)-f(a)/b-a

Find instantaneous rate of change of f(x) at a

Find f’(a)

Find the average of f(x) on [a,b]

Find int from b to a of f(x) divided by b minus a

Given s(t) - position function, find v(t)

Find v(t)= s’(t)

Given v(t), find how far a particle travels on [a,b]

Find int from a to b of absolute value of v(t) dt

Find the average velocity of a particle on [a,b]

Find average rate of change = s(b) - s(a)/(b-a)

Given v(t) determine if a particle is speeding up at t=k

Find v(k) and a(k). Multiply their signs. If both are positive, the particle is speeding up, and if they’re different signs, then the particle is slowing down

Given v(t) and s(0), find s(t)

s(t)= int v(t)dt+ C, plug in to find C

Show that Rolle’s Theorem holds on [a,b]

Show that f is continuous and differentiable on the interval. If f(a)=f(b) then find a c in [a,b] such that f’(C) = 0

Show that mean Value Theorem holds on [a,b]

Show that f is continuous and differentiable on the interval. then find a c such that f’(c ) = f(b)-f(a)/b-a

find f’(x) by definition

f’(x)= lim h→0 f(x+h)-f(x)

d/dx int f(t)

f(x)

the rate of change of population is

dP/dt

The line y=mx+b is tangent to f(x) at (x1,y1)

the two functions share the same slope and the same y value at x1

Find area using left Riemann sums

A = b-a/n [f(0)+f(1)+f(2)+f(3)]

Find area using right Riemann sums

A = base [f(1)+f(2)+f(3)+f(4)]

Find area using midpoint rectangles

Use only given values, use half of the number of sets of points

Find area using trapezoids

A= base/2 [x0+2×1+2×2+2xn-1 +xn]

Solve the differential equation

Separate the variables x on one side and y on the other the dy and dx must be in numerator

Meaning of int f(t) dt

Accumulated area under the function of f(x) starting at a constant a and ending at x

Given a base, cross sections perpendicular to the x axis are squares

The area between the curves, volume is int (base²) dx

Find where the tangent line to f(x) is horizontal

Write f’(x) as a fraction. Set the numerator equal to zero

Find where the tangent line to f(x) is vertical

Write f’(x) as a fraction. Set the denominator equal to zero

Find the derivative of f(g(x))

f’(g(x)) * g’(x)

Given int from a to b of f(x), find int from a to b of f(x)+k

Set int f(x)+k equal to int f(x) to int k

Given an image of f’(x), find where f(x) is increasing

Determine where f’(x) is positive

Given a water tank with g gallons being filled at a rate of F(t) and emptied at E(t) on interval, find the amount of water in the tank at m minutes

gallons+ int F(t)- E(t)

[Gallons problem] the rate the water amount is changing at m

d/dt int F(t) - E(t) = F(m) - E(m)

[Gallons problem] find the time when the water is at a minimum

Test the endpoints and find where F(m) - E(m) = 0

Find the area between curves f(x) and g(x) on [a,b]

A = int [f(x)-g(x)]dx assuming that f is above g

Find the volume of the area between f(x) and g(x) is rotated about the x axis

A = int f(x)² - g(x)² assuming that f is above g