How do you find the maximum value of a function?

Substitute the critical number x = 2 in f”(x). So, f(x) is maximum at x = 2. To find the maximum value, substitute x = 2 in f(x). Therefore the maximum value of the function f(x) is 7.

What are the minimum and maximum values of the function f/x )= x 3 on the interval [- 3 2?

Evaluate ddx[−3×2] d d x [ – 3 x 2 ] . Since −3 – 3 is constant with respect to x x , the derivative of −3×2 – 3 x 2 with respect to x x is −3ddx[x2] – 3 d d x [ x 2 ] . Differentiate using the Power Rule which states that ddx[xn] d d x [ x n ] is nxn−1 n x n – 1 where n=2 n = 2 . Multiply 2 2 by −3 – 3 .

What is the maximum value of 3 7cos5 X?

The maximum value of 3 – 7 cos 5 x is 10.

How do you find the maximum or minimum value of a function?

Finding max/min: There are two ways to find the absolute maximum/minimum value for f(x) = ax2 + bx + c: Put the quadratic in standard form f(x) = a(x − h)2 + k, and the absolute maximum/minimum value is k and it occurs at x = h. If a > 0, then the parabola opens up, and it is a minimum functional value of f.

What is the minimum and maximum value of 4 5sin 3x 2?

So maximum value of question is 9. Hope this helps.

What is the maximum value of cos COSX?

1
Note: Cosine is a decreasing function from o to $\pi$. It has maximum value 1 when $x={{0}^{\circ }}$ and minimum value -1 when $x={\pi }$. So we can also say \[\cos (\cos x)\] will have a maximum value when cos(x) has value 0.

What is the maximum value of log?

If the base of the logarithm is e , one can say log(x)/x takes maximum at e . If the base of the logarithm is 10 , one can say log(x)/x takes maximum at 10 .

What is the maximum value of Sinx COSX?

Maximum value of sin(2x) is at x = 45° because sin 90° = 1 (max). Therefore, maximum value of sin(x)cos(x) = (1/2)×1 = 1/2 or 0.5.

What is the maximum and minimum value of f(x)?

The function f (x) is maximum when f” (x) < 0 The function f (x) is minimum when f” (x) > 0 To find the maximum and minimum value we need to apply those x values in the original function.

What is the critical value of 3×2 – 3 = 0?

The critical values are when 3×2 − 3 = 0, which simplifies to be x = ± 1. However, x = − 1 is not in the interval so the only valid critical value here is the one at x = 1.

How to find the maximum and minimum value of a derivative?

Apply those critical numbers in the second derivative. To find the maximum and minimum value we need to apply those x values in the original function. To find the maximum value, we have to apply x = 2 in the original function. Therefore the maximum value is 7 at x = 2. Now let us check this in the graph.

Does the function have an absolute maximum and an absolute minimum?

So, the function does not have an absolute maximum. Note that it does have an absolute minimum however. In fact the absolute minimum occurs twice at both x =−1 x = − 1 and x =1 x = 1. the function would now have both absolute extrema.