Question

1. if ( f(x)=x^{\frac{3}{2}} ), then ( f^{prime}(4)= ) a -6 b -3 c 3 d 6 e 8

Explanation:

Step1: Differentiate the function

Use the power rule \( (x^n)^\prime=nx^{n - 1} \). For \( f(x)=x^{\frac{3}{2}} \), \( f^\prime(x)=\frac{3}{2}x^{\frac{3}{2}-1}=\frac{3}{2}x^{\frac{1}{2}} \).

Step2: Substitute \( x = 4 \) into the derivative

When \( x = 4 \), \( f^\prime(4)=\frac{3}{2}\times4^{\frac{1}{2}} \). Since \( 4^{\frac{1}{2}}=\sqrt{4} = 2 \), then \( f^\prime(4)=\frac{3}{2}\times2=3 \).

Answer:

C. 3