question :) (1 Viewer)

[izzy_xo]

i can't work out this question :|

The tangent to the curve y=ax^3+2 at the point where x=3 is inclined at 135degrees to the x-axis. Find the value of a.

Any help would be greatly appreciated

 

[Uncle]

I worked out this problem in 3 seconds but hopefully it should be the case.

Definition of the gradient function, derivative, slope, etc. same thing.

[maths]m = \frac{\mathrm{dy} }{\mathrm{d} x} = tan \theta[/maths]

y = ax³ + 2

[maths]\frac{\mathrm{dy} }{\mathrm{d} x} = 3ax^{2}[/maths]


Given x = 3 and [maths]\theta[/maths] = 135⁰

3a(3)² = tan 135⁰

[maths]a = \frac{tan 135^{\circ}}{27}[/maths]

 

[izzy_xo]

hey thanks,
but the answers in the book say a=-1/27
hmm

 

[Uncle]

hey thanks,
but the answers in the book say a=-1/27
hmm

Just found a calculator.
tan 135⁰ = -1

o rly?

YAY!

 

[izzy_xo]

hahahaaha thankss
clearly can't think straight today