Please show work: Show that the function f(x) = x^4 + 8x + 6 has exactly one zer
ID: 2849482 • Letter: P
Question
Please show work:
Show that the function f(x) = x^4 + 8x + 6 has exactly one zero in the interval [ -1, 0]. Which theorem can be used to determine whether a function f(x) has any zeros in a given interval? A. Intermediate value theorem B . Extreme value theorem C. Mean value theorem D. Rolle?s Theorem To apply this theorem, evaluate the function f(x) = X^4 + 8x + 6 at each endpoint of the interval [-1, 0]. f( -1) = L (Simplify your answer.) f(0) = L (Simplify your answer.) According to the intermediate value theorem, f(x) = x4 + 8x 6 has [j in the given interval. Now, determine whether there can be more than one zero in the given interval. Rolle?s Theorem states that for a function f(x) that is continuous at every point over the closed interval [a,b] and differentiable at ever point of its interior (a,b), if f(a) = f(b), then there is at least one number e in (a,b) at which f?(c) = 0. Find the derivative of f(x) = x^4 + 8x + 6. f?(x) = Can the derivative of f(x) be zero in the interval [- 1, 0)? No YesExplanation / Answer
extreme value theorem
f(-1) = -1
f(0)= 6
f'( x) = 4x^3 +8
yes