The equation of a curve is given by

Question

y = (2x+5)+(x^2+1)*ln(2x^2+Ax+2) where A is a constant.? 

 

a) Calculate the slope of the tangent line to the curve at point x (Do not simplify) 

b) Calculate the value of A so that the slope of the tangent line to the curve at x=0 is 4

 

Answer 1

(a)

The Equation of the curve is y = (2x + 5) + (x² + 1) * ln(2x² + Ax + 2).

To Find the slope of the line, we differentiate y with respect to x.

Therefore Slope of the tangent line Equation is

Answer 2

(b)

The Equation of the curve is y = (2x + 5) + (x² + 1) * ln(2x² + Ax + 2).

To Find the slope of the line, we differentiate y with respect to x.

Slope of the tangent at x = 0 is 4

2 = A/2

A = 4

Therefore the value of A is 4.