Question: a. Given that a x e kx , where a and k are constants, a > 0 and x R, prove that k

a. Given that ax ≡ ekx, where a and k are constants, a > 0 and x ∈ R, prove that k = ln a.

b. Hence, using the derivative of ekx, prove that when y = 2x dy/dx = 2x ln 2

c. Hence deduce that the gradient of the curve with equation y = 2x at the point (2, 4) is ln 16.

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