Calculus Final Exam - Average Rate of Change, Tangent Lines and Derivatives

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10 Terms

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The figure presents the graphs of two lines in the x y coordinate plane, with the origin labeled O. The numbers negative 5 through 5, in increments of 1, are indicated on the x axis. The numbers negative 1 through 9, in increments of 1, are indicated on the y axis. One line is labeled y equals f of x, and the other line is labeled y equals g of x. The line labeled y equals f of x slants upward and to the right, and passes through the point with coordinates negative 2 comma negative 1, crosses the x axis at negative 1, crosses the y axis at 1, and passes through the point with coordinates 3 comma 4. The line labeled y equals g of x slants downward and to the right, and passes through the point with coordinates negative 3 comma 4, crosses the y axis at 2, and crosses the x axis at 3. The two lines intersect at the point with approximate coordinates one half comma 1.5.

The graphs of the linear functions f and g are shown above. If ℎ(x)=f(x)+g(x), then h’(x) =

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Let f be the function defined by f(x)=2sinx+cosx. The average rate of change of f over the interval [0,b] is 0.05, where b>0. Which of the following is an equation that could be used to find the value of b ?

A) f(b) = 0.05

B) f(b) - f(0) = 0.05

C) ( f(b) - f(0) ) / (b - 0) = 0.05

C) ( f(b) + f(0) ) / (2) = 0.05

C) ( f(b) - f(0) ) / (b - 0) = 0.05

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four

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14

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II and III only

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57

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-8

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