Gradient Ascent Problem Calculus

Question

Suppose we apply gradient ascent algorithm to find a local maximum of the function f(x,y) = 3x cos^3 *y + 1/x. If we start from the point (x0,y0) = (−1, π/3 ) and use learning rate α = 0.1 to go uphill as high as possible (initially), what point (x1,y1) will we end up at after the first step?

I have no idea how to solve this and can't find algebraic methods online with an explanation or theorem. This is the answer: ≈(−1.0625,1.2421) but again I don't know the logic behind it.

Answer 1

Gradient ascent formula

New value=old value + α∇f(old value)

α is rate change.

∇f(x,y)=<3cos³y- 1/x², -9xcos²ysiny>∇

∇f(-1,π/3)=<3(1/8) - 1/1, -9(-1)(1/4)(√3/2)> or

<-5/8, 9√3/8>

0.1×∇f(-1,π/3)=<-0.0625,0.1949>

New value=(-1 - 0.0625, π/3 +0.1949)

New value=(-1.0625, 1.2421)