Find the x-values of all points where the function has any relative extrema. Fin

Question

Find the x-values of all points where the function has any relative extrema. Find the value(s) of any relative extrema. f(x)= 14x+15x14/15 nd rcyi a doice ( A. There are no relative minima. The function has a relative maximum of (Use a comma to separate answers as needed.) There are no relative maxima. The function has a relative minimum of (Use a comma to separate answers as needed.) The function has a relative maximum of (Use a comma to separate answers as needed.) There are no relative extrema. at. 0 B. at x = C. at x' and a relative minimum of at x D.

Explanation / Answer

Dear Student Thank you for using Chegg !! Given f(x) = 14x + 15x^ (14/15) Differentiating w.r.t x and using identity d/dx (x^n) = nx^(n - 1) We get f'(x) = 14 + 14x^(-1/15) = 0 x^ (-1/15) = -1 Now taking 15th power at both sides we get x = -1 Now double differentiating f(x) we get f''(x) = -(14/15)x^(-16/15) which shall be always positive Hence f(x) will have a relative maxima at at x = -1 f(-1) = -14 + 15*(-1)^(14/15) = -14 -15 =-29 Solution

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