The graph of a function f is shown. Which graph is an antiderivative of f? F

philosphy111of 2021-11-18 Answered
The graph of a function f is shown. Which graph is an antiderivative of f?
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Coldst
Answered 2021-11-19 Author has 18 answers
Step 1
Let g(x) be the antiderivative of f(x). Then we must have
g(x)=f(x)dx
g(x)=f(x)
Now, since f(x) is negative (, p) that means the g(x) is negative in this interval. So, g(x) (the antiderivative of f(x) must be decreasing in this interval. This scenario is shown in two graphs a and b.
Again we notice that f(x) is positive that means, g(x) is positive in (p, ). So, the function g(x)= antiderivative of f(x) must be increasing in this interval and from the graph we can see that the graph b is increasing after the point x=p.
So, the correct graph for the antiderivative of f(x) is b.
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