which theorem can be used to determine whether a function f(x) has any zeros in a given interval?\na…

which theorem can be used to determine whether a function f(x) has any zeros in a given interval?\na. intermediate value theorem\nb. extreme value theorem\nc. rolles theorem\nd. mean value theorem\nto apply this theorem, evaluate the function f(x) = x⁴ + 5x + 3 at each endpoint of the interval -1, 0.\nf(-1) = -1 (simplify your answer.)\nf(0) = (simplify your answer.)

which theorem can be used to determine whether a function f(x) has any zeros in a given interval?\na. intermediate value theorem\nb. extreme value theorem\nc. rolles theorem\nd. mean value theorem\nto apply this theorem, evaluate the function f(x) = x⁴ + 5x + 3 at each endpoint of the interval -1, 0.\nf(-1) = -1 (simplify your answer.)\nf(0) = (simplify your answer.)

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 )