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

The maximum will occur at the highest f (x) f ( x) value and the minimum will occur at the lowest f (x) f ( x) value.

What is the derivative at x = 0x = 0?

The final answer is − 12 – 12. At x = 0 x = 0 the derivative is − 12 – 12. Since this is negative, the function is decreasing on ( − 2, 2) ( – 2, 2). Substitute a value from the interval (2,∞) ( 2, ∞) into the derivative to determine if the function is increasing or decreasing. Tap for more steps…

How do you find the absolute extrema of a function?

Use the endpoints and all critical points on the interval to test for any absolute extrema over the given interval. Evaluate the function at x = 0 x = 0. Simplify the right side. Tap for more steps… Simplify each term. Tap for more steps… Raising 0 0 to any positive power yields 0 0. Raising 0 0 to any positive power yields 0 0.

Is the function increasing or decreasing on – ∞ – 1?

Since this is positive, the function is increasing on ( − ∞, − 1) ( – ∞, – 1). Substitute a value from the interval (−1,3) ( – 1, 3) into the derivative to determine if the function is increasing or decreasing.

What is the exact value of sin( π2) sin(Pi2)?

The exact value of sin ( π 2) sin ( π 2) is 1 1. Multiply − 9 – 9 by 1 1. x = π 6 x = π 6 is a local maximum because the value of the second derivative is negative. This is referred to as the second derivative test. Find the y-value when x = π 6 x = π 6. Tap for more steps… Replace the variable x x with π 6 π 6 in the expression.

How do you find the local maximum and minimum of 3x?

Rewrite the expression. The solution to the equation 3x = π 2 3 x = π 2. Evaluate the second derivative at x = π 6 x = π 6. If the second derivative is positive, then this is a local minimum. If it is negative, then this is a local maximum.

What is the range of h[x] + sin[y] + sine[x+y]?

The function h [x,y] = Sin [x] + Sin [y] + Sin [x+y] is the sum of three sine wave functions. Each has values in the range {-1,1}. As noted in an earlier answer, if they all peaked at the same point, the range of h [x,y] would lie in {-3,3}. I like to look a graphic versions of problems like this one.

How to solve an equation with a value of 0?

If any individual factor on the left side of the equation is equal to 0 0, the entire expression will be equal to 0 0. Set the first factor equal to 0 0. Set the next factor equal to 0 0 and solve. Tap for more steps… Set the next factor equal to 0 0.

How to find the critical values of a function?

The critical values can be found by finding the function’s derivative and finding for which values of x it equals 0. We can use the power rule to find that the derivative of f (x) = x3 − 3x + 1 is f ‘(x) = 3×2 −3. The critical values are when 3×2 − 3 = 0, which simplifies to be x = ± 1.

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.