Suppose that ƒ has a positive derivative for all values of

Chapter 5, Problem 81E

(choose chapter or problem)

Suppose that $f$ has a positive derivative for all values of $x$ and that $f(1) = 0$. Which of the following statements must be true of the function

$g(x)=\int_{0}^{x} f(t) d$

Give reasons for your answers.

a. $g$ is a differentiable function of $x$.

b. $g$ is a continuous function of $x$.

c. The graph of $g$ has a horizontal tangent $x = 1$.

d. $g$ has a local maximum at $x = 1$.

e. $g$ has a local minimum at $x = 1$.

f. The graph of $g$ has an inflection point at $x = 1$.

g. The graph of $dg/dx$ crosses the $x$-axis at $x = 1$.

Equation Transcription:

$f$

$x$

$f(1)=0$

$g(x)=\int\limits_{0}^{x}f(t)d$

$g$

$x=1$

$dg/dx$

Text Transcription:

f(1)=0

g(x)= integral_0^x f(t)d

x=1

dg/dx

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