Let g(x) =
where f is shown at right. Homework Help ✎
Find g(2) and g(4).
Is g(−2) =
in terms of g.
Is g differentiable over the interval −2 < x < 6 ? Explain.
Find all values of x on the interval −2 < x < 6 where g has a relative maximum.
Find the line tangent to g at x = 4.
Find all values of x on the interval −2 < x < 6 where g has a point of inflection.
Consider the symmetry of the f(t) between t = −2 and t = 2.
What is k? What is a?
Points of NON-differentiablity include cusps, endpoints, jumps, holes and vertical tangents.
Recall that a local maximum exists where the derivative changes from positive to negative. This could happen where f '(x) = 0 or where f '(x) = DNE.
Notice that g'(x) = f(x); after all, the derivative of an integral is the original function.
What is the slope of g(x) at x = 4 (see second hint in part (e))? What is the y-value?
Concavity is the slope of the slope. So inflection points are where the slope of the slope changes.