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2 years ago

9

Help with calculus please?

1 answer:

Kazeer [188]2 years ago

3 0

Wait let me know that the .12 means in the first question and i will fix the answer

int (x)(cosx) dx

u=x ----> take derivative du=dx
dv=cosx -----> take integral v=sinx

now use integration by parts

u v - int (v)du
x sinx - int (sinx) (1) dx=

x sinx - (-cos(x)) + c =

answer is = x sinx + cosx + c

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Using the critical point concept, it is found that a = -3 and b = 7.

<h3>What are the critical points of a function?</h3>

The critical points of a function are the values of x for which:

$f^{\prime}(x) = 0$

In this problem, the function is:

$f(x) = x^3 + ax^2 + b$

Hence, the derivative is:

$f^{\prime}(x) = 3x^2 + 2ax$

Then:

$f^{\prime}(x) = 0$

$3x^2 + 2ax = 0$

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$x = 0$

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Since the critical point is at x = 2, we have that:

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$-2a = 6$

$2a = -6$

$a = -3$

Then:

$f(x) = x^3 - 3x^2 + b$

Critical point at (2,3) means that when $x = 2, y = 3$ , then:

$3 = 2^3 - 3(2)^2 + b$

$8 - 12 + b = 3$

$b = 7$

You can learn more about the critical point concept at brainly.com/question/2256078

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