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

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 ( -(1)/(3)\right,2 )`