Question

f(x)= 5x^3 and 135x-y=6=0 find and equation of a line that is tangent to the graph of f and parallel to the given line

Answer 1

pl verify eqn of line
135x-y=6=0

Answer 2

there are 2 equal signs

Answer 3

oh im sorry its 135x-y+6=0

Answer 4

given line's equation is y = 135x+6 (or -6, I don't know what you meant!)
So we need to find point in f(x) whose gradient is 135.

f'(x)=15x^2 = 135
x^2 = 9
x = 3 or x = -3

When x = 3, f(x) = 5(3^3) = 135.

Equation of line is y = 135x + c
But 135 = 135(3) + c
Hence c = 135 - 135(3) = -270

One good line would thus be y = 135x - 270.

Answer 5

Another good line would have x = -3, so f(x) would be 5(-3)^3 = -135 in that case.

The line would still have gradient 135. So y = 135x + c
But -135 = 135(-3) +c
c = -135 + 135(3) = 270

Hence another good line would be y = 135x + 270.