find the critical points of the following function.\nf(x)=4x^{2}+3x - 5\nselect the correct choice below…

find the critical points of the following function.\nf(x)=4x^{2}+3x - 5\nselect the correct choice below and, if necessary, fill in the answer box to complete your choice.\na. the critical point(s) occur(s) at x=\n(use a comma to separate answers as needed.)\nb. there are no critical points.

find the critical points of the following function.\nf(x)=4x^{2}+3x - 5\nselect the correct choice below and, if necessary, fill in the answer box to complete your choice.\na. the critical point(s) occur(s) at x=\n(use a comma to separate answers as needed.)\nb. there are no critical points.

Answer

Explanation:

Step1: Find the derivative of the function

Using the power rule ((x^n)^\prime = nx^{n - 1}), for (f(x)=4x^{2}+3x - 5), the derivative (f^\prime(x)=(4x^{2})^\prime+(3x)^\prime-(5)^\prime). (f^\prime(x)=4\times2x+3\times1 - 0=8x + 3).

Step2: Set the derivative equal to zero and solve for (x)

Set (f^\prime(x)=0), so (8x+3 = 0). Subtract (3) from both sides: (8x=-3). Divide both sides by (8): (x =-\frac{3}{8}).

Answer:

A. The critical point(s) occur(s) at (x =-\frac{3}{8})