Question

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. rolles theorem
d. mean value theorem
to apply this theorem, evaluate the function f(x) = x⁴ + 5x + 3 at each endpoint of the interval -1, 0.
f(-1) = -1 (simplify your answer.)
f(0) = (simplify your answer.)

Explanation:

Step1: Evaluate \( f(0) \)

Substitute \( x = 0 \) into \( f(x)=x^{4}+5x + 3 \).
\( f(0)=0^{4}+5\times0 + 3\)

Step2: Simplify the expression

\( f(0)=0 + 0+3\)

Answer:

\( 3 \)