The function f(x) = x^3 − x + 4, in continuous in the interval [1, 2]. Find the value of ‘x' at which the function takes the value 7. (Hint: Use f(x) = 7)

2

Step-by-step explanation:

Given the function

f(x) = x^3 − x + 4 in the interval [1,2]

We are to find the value of x for which f(x) = 7

Substitute f(x) = 7 into the expression as shown!

f(x) = x^3 − x + 4

7 = x^3 − x + 4

x^3 − x + 4 -7 = 0

x^3 − x - 3= 0

x^3 -x = 3

x(x²-1) = 3

x²-1 = 3 and x = 3

x² = 3+1

x² = 4

x = ±√4

x = ±2

Since x lies within the interval, [1,2] hence the value of x is 2