(1) Find the critical points of the function g(x) below and evaluate the value of the function at the critical points and the end-points of the interval to calculate the absolute minimum and the maximum. g(x) = x³ — 48x in the interval [—–5,5].

Q: Let f(x)= 3x(x-1)2 be a function defined on the interval [1,∞). Find the solution to f(x)= 78.

A: Given, f(x)= 3x(x-1)2 be a function in [1,∞). We need to find the solution to the equation f(x)= 78

Q: Find the maximum point for the function f(x) = 1 + 12x – 4x O (-1, -7) O (2, -7) O (0, 1) (1, 9)

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Q: b- Determine the critical point of the function f(x) = x5 – 5x* + 5x³ –- 1 %3D

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Q: Find the absolute maximum and absolute minimum of the function f(r) =r² - 8z+7 over [1, 8].

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Q: kimum and minimum r3 9y +1

A: Given as, f(x)=x3 -9x+1, -∞,∞

Q: identify the coordnates of any local maximum or minmum values of the function y=(x+3)2/ e2x

A: y=(x+3)2/ e2x Or, y = (x+3)2e-2x We need to find it's derivative and equate the same to zero.

Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = x3 – 3x +…

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Q: Find the maximum and minimum points of f(x) = x(12 – x)?

A: topic - application of derivatives