The maximum value of the function f(x) = x^{3 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let $f(x) = x^{3} - 12x^{2} + 36x + 17$. Find the derivative: $f'(x) = 3x^{2} - 24x + 36$. Set $f'(x) = 0$ to find critical points: $3(x^{2} - 8x

Vedclass · Accepted Answer

$177$

Vedclass · Answer

(B) Let $f(x) = x^{3} - 12x^{2} + 36x + 17$. Find the derivative: $f'(x) = 3x^{2} - 24x + 36$. Set $f'(x) = 0$ to find critical points: $3(x^{2} - 8x + 12) = 0 \Rightarrow 3(x - 2)(x - 6) = 0$. The critical points are $x = 2$ and $x = 6$. Evaluate the function at the critical points and the interval endpoints $[1, 10]$: $f(1) = (1)^{3} - 12(1)^{2} + 36(1) + 17 = 1 - 12 + 36 + 17 = 42$. $f(2) = (2)^{3} - 12(2)^{2} + 36(2) + 17 = 8 - 48 + 72 + 17 = 49$. $f(6) = (6)^{3} - 12(6)^{2} + 36(6) + 17 = 216 - 432 + 216 + 17 = 17$. $f(10) = (10)^{3} - 12(10)^{2} + 36(10) + 17 = 1000 - 1200 + 360 + 17 = 177$. Comparing these values,the maximum value is $177$.

The maximum value of the function $f(x) = x^{3} - 12x^{2} + 36x + 17$ in the interval $[1, 10]$ is:

Similar Questions

If $x=-2$ and $x=4$ are the extreme points of $y=x^3-\alpha x^2-\beta x+5$,then

The function $f(x) = \frac{\sin(x + a)}{\sin(x + b)}$ has no maxima or minima if

If the absolute maximum and absolute minimum values of the function $f(x) = x^3 - 2x^2 + x - 3$ defined on $[0, 2]$ are $M$ and $m$ respectively, then $M + m =$

$A$ triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having a fence are of the same length $x$. The maximum area (in sq. units) enclosed by the park is

All the points on the curve $y^{2}=4a|x+a \sin(x/a)|$,where the tangent is parallel to the $x$-axis,lie on:

Vedclass Test Series

Exam Paper Generator

Online Exam Module