How do you find the exact relative maximum and minimum of the polynomial function of #f(x) = x^36x^2+15#?
Relative maximum:
Relative minimum:
By signing up, you agree to our Terms of Service and Privacy Policy
To find the exact relative maximum and minimum of the polynomial function f(x) = x^3  6x^2 + 15:

Take the derivative of the function f(x) to find critical points. f'(x) = 3x^2  12x

Set the derivative equal to zero and solve for x to find critical points. 3x^2  12x = 0 x(3x  12) = 0 x = 0 or x = 4

Evaluate the function at the critical points and endpoints to find the yvalues. f(0) = 15 f(4) = 15

Determine the nature of the critical points using the second derivative test. f''(x) = 6x  12
For x = 0: f''(0) = 12 Since f''(0) < 0, it indicates a relative maximum at x = 0.
For x = 4: f''(4) = 12 Since f''(4) > 0, it indicates a relative minimum at x = 4.

Therefore, the exact relative maximum is (0, 15) and the exact relative minimum is (4, 15).
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
 How do you determine whether the function #f(x) = (x^2)/(x^2+1)# is concave up or concave down and its intervals?
 Is #f(x)=(x1/x)# concave or convex at #x=1#?
 Is #f(x)=9x^5+15x^421x^28x+2# concave or convex at #x=3#?
 How do you find the x coordinates of all points of inflection, final all discontinuities, and find the open intervals of concavity for #f(x)=x^48x^3#?
 Is #f(x)=x^5+3x^49x^32x^26x# concave or convex at #x=8#?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7