Question

Let $f(x) = 3x^5 - 10x^3 + 15x + a$, where $a$ is some constant. (a) (2 points) Prove that, regardless of the value $a$, $f'(x) > 0$ for all $x$ in $(-1, 1)$. (b) (2 points) Prove that, regardless of the value $a$, the equation $f(x) = 0$ does not have two distinct roots in $[-1, 1]$.

          Let $f(x) = 3x^5 - 10x^3 + 15x + a$, where $a$ is some constant.
(a) (2 points) Prove that, regardless of the value $a$, $f'(x) > 0$ for all $x$ in $(-1, 1)$.
(b) (2 points) Prove that, regardless of the value $a$, the equation $f(x) = 0$ does not have two
distinct roots in $[-1, 1]$.

Let f(x) = 3x^5 - 10x^3 + 15x + a, where a is some constant.
(a) (2 points) Prove that, regardless of the value a, f'(x) > 0 for all x in (-1, 1).
(b) (2 points) Prove that, regardless of the value a, the equation f(x) = 0 does not have two
distinct roots in [-1, 1].

Added by Craig C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

09/24/2023

Step 1

Step 1: First, let's find the derivative of f with respect to x, denoted as f'. Show more…

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Let f=3x-10x+15x+a, where a is some constant. (a) (2 points) Prove that, regardless of the value a, f') > 0 for all x in (-1,1). b)2 points) Prove that,regardless of the value a,the equation f(=0 does not have two distinct roots in [-1,1].