Question

How many critical values does the function f(x) = 3x^4 + 4x^3 have? none one two three four The function y = x^3 + 15 x^2 - 33 x has a relative maximum when x = -11. 11. 0. -1. 1. The function f(x) = 4x^3 - 10x^2 - 8x + 3 is decreasing on (-infinity, 2). (-1/3, infinity). (-1/3, 2). (2, infinity). (-infinity, 1/3).

Answer 1

Answer:Given below

Step-by-step explanation:

Given

$F\left ( x\right )=3x^4+4x^3$

To find critical values $F'\left ( x\right )=0$

$4\cdot 3x^3+3\cdot 4x^2=0$

$12x^2\left ( x+1\right )=0$

therefore x=-1,0 are two critical points

$\left ( b\right )$

$F\left ( x\right )=x^3+15x^2-33x$

To find maxima/minima $F'\left ( x\right )=0$

$3x^2+30x-33=0$

$x^2+10x-11=0$

$\left ( x-1\right )\left ( x+11\right )=0$

x=1,-11

For maxima $F''\left ( x\right )<0$

for x=-11, $F''\left ( x\right )<0$

$\left ( c\right )$

$F\left ( x\right )=4x^3-10x^2-8x+3$

For decreasing curve $F'\left ( x\right )<0$

$12x^2-20x-8<0$

$3x^2-5x-2<0$

$\left ( 3x+1\right )\left ( x-2\right )<0$

therefore x is decreasing in interval $\left ( -\frac{1}{3}\right,2 )$