Hi, can someone help me with these 4 calculus problems please? More points will

Question

Hi, can someone help me with these 4 calculus problems please? More points will be given to those who provide an explanation. Thank you!

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Find the equation of the tangent line to the curve y = 4 secx - 8 cos x at the point (pi/3, 4). The equation of this tangent line can be written in the form y = mx + b where m is: Find the equation of the tangent lie to the curve y = 4x cos x at the point (pi, -4 pi). The equation of this tangent line can be written in the form y = mx + b where For what values a and b is the line-4x + y = b tangent to the curve y = ax3 when x = -5?

Explanation / Answer

2.

Given, y = 4xcosx

Now, tangent = dy/dx = 4cosx - 4xsinx

at point(pi,-4pi) = dy/dx = 4(-1) -4pi(0)

= -4

At the point (pi,-4pi), equation of line is

(y-y1) = m(x-x1)

So, y - (-4pi) = -4 (x - pi)

=> y = -4x + 4pi - 4pi

or, y = -4x

So, m = -4 and b = 0

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