Consider the function f(x)=7x^(2)+9.

Question

Its tangent line at x=5 goes through the points (1,y1) and (−7,y2) where y1= ___ , and y2= ___

Answer 1

y = 7x^2 + 9
dy/dx = 14x which is the slope of the tangent
so when x = 5, slope = 70
and y = 7(25) + 9 = 184

so the tangent has a slope of 70 and goes through the point (5,184)

equation of tangent:
y - 184 = 70(x-5)
y = 70x - 166

to get y1, replace x with 1
to get y2, replace x with -7

Answer 2

Thank you very much! I was stuck and needed this.