Question

Show that the function f(x) = x4 + 3x + 1 has exactly one zero on the
interval [−2,−1].

Answer 1

Take the derivative.

Answer 2

MVT

Answer 3

afterthat what can we proof is there a 0 point between domain

Answer 4

how can sorry

Answer 5

can you explain the solution by writing step by step? :) it's urgent :(

Answer 6

derivative is 4x^3 + 3
4x^3 + 3 < 0 for negative gradient
x^3 < -3/4
x < (-3/4)^(1/3) = approx -0.9
this is greater than -1 so the graph is decreasing over the period -2,-1

find value of function atx = -2 and -1

f(-2) = (-2)^4 + 3(-2) + 1 = 11
f(-1) = -2

meaning it has crossed the x-axis at most once over the period

Answer 7

thank u for solution crw238 :)