f is given by f(x)=1/7x7+1/2x6-x5-15/4x4+4/3x3+6x2. What is true?

Question

f is given by f(x)=1/7x⁷+1/2x⁶-x⁵-15/4x⁴+4/3x³+6x². What is true?

A)f')-3.1) < f'(-1.5) < f'(0.4)

B) f'(3.1) < f'(0.4) < f'(-1.5)

C) f'(-1.5) < f'(0.4) < f'(-3.1)

D) f'(0.4) < f'(1.5) < f'(-3.1)

Answer 1

Let's calculate the first derivative of f(x) following (xⁿ)'=nx^n-1

f'(x) = x⁶+3x⁵-5x⁴-15x³+4x²+12x

Now we can calculate values of ineterest

f'(-3.1) = 14.973651

f'(-1.5) = 4.921875

f'(0.4) = 4.386816

f'(1.5) = -14.765625

f'(3.1) = 913.392711

According to this none of the given options A to D is true. There could be a typo in the given statements. Assuming that 0.4 only does not have a negative value answers A and B are eliminated since f'(0.4)<f'(-3.1) and f'(0.4)<f'(-3.1).

C could be true if it was stated as f'(1.5) < f'(0.4) < f'(-3.1).

D could be true if it was stated as f'(0.4) < f'(-1.5) < f'(-3.1).

Please check your original statements C and D.