Question

5.1 Let \( f(x)=2 x^{3}-3 x^{2}-72 x+15 \). (a) Find the relative extrema values of \( f(x) \) using the first derivative test. (b) Determine the open interval on which the function \( f(x) \) is increasing and decreasing. (c) Find \( f^{\prime \prime}(x) \).

          5.1 Let \( f(x)=2 x^{3}-3 x^{2}-72 x+15 \).
(a) Find the relative extrema values of \( f(x) \) using the first derivative test.
(b) Determine the open interval on which the function \( f(x) \) is increasing and decreasing.
(c) Find \( f^{\prime \prime}(x) \).

5.1 Let f(x)=2 x^3-3 x^2-72 x+15.
(a) Find the relative extrema values of f(x) using the first derivative test.
(b) Determine the open interval on which the function f(x) is increasing and decreasing.
(c) Find f^''(x).

Added by Juan Antonio B.

Essential Calculus Early Transcendentals

James Stewart 2nd Edition

Chapter 4

Instant Answer

Solved by Expert Kathleen Carty

Step 1

Given \( f(x) = 2x^3 - 3x^2 - 72x + 15 \), the first derivative \( f'(x) \) is found by differentiating \( f(x) \) with respect to \( x \). This gives: \[ f'(x) = \frac{d}{dx}(2x^3) - \frac{d}{dx}(3x^2) - \frac{d}{dx}(72x) + \frac{d}{dx}(15) \] \[ f'(x) = 6x^2 - Show more…

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5.1 Let \( f(x)=2 x^{3}-3 x^{2}-72 x+15 \). (a) Find the relative extrema values of \( f(x) \) using the first derivative test. (b) Determine the open interval on which the function \( f(x) \) is increasing and decreasing. (c) Find \( f^{\prime \prime}(x) \).