# -apc.4.2.9 graph of f(x) to g(x)

• MHB
Gold Member
MHB image due to graphs

ok just by observation I chose D since integrals tend to introduce curves not eliminate them and the slope was positive

skeeter
two significant typos in this problem ...

(1) should be $\displaystyle g(x) = \int_2^x f(t) \, dt$,

(2) which of the following could be $y=g(x)$, not $g(f)$

$g’(x) = f(x) \implies$ the graph of $f(x)$ is the graph of the derivative of $g(x)$

so ... what do you think?

Gold Member
MHB
good catch

HOI
https://www.physicsforums.com/attachments/10736
image due to graphs

ok just by observation I chose D since integrals tend to introduce curves not eliminate them and the slope was positive
You should be able to say much more than that! Since the graph of f is a straight line, f is "linear" and its integral is quadratic so its graph is a parabola. Further since the graph of f is below the x-axis the integral starts out negative and becomes positive. Yes, the slope of f is positive so the curvature of g is positive. THAT is why "D" is the correct choice!

skeeter Gold Member
MHB
graphs always help a lot

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MHB
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HOI
"WIP', "PDF", "AP"? I thought we were supposed to use English on this site!

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MHB
WIP Work In Progress

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