(another characterisation of y = e^x -- it is the only exponential function whose gradient at its y-intercept is 1)
(a) prove that y= a^x has derivative at y=a^x loga
(b) prove that y= a^x has gradient 1 at its y intercept if and only if a = e
(c) prove that y=Aa^x has gradient 1 at its y intercept if and only if a=e^(1/a)

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