Question

find the gradient of the tangent of f(x)=x^1/2 by using first principles.

Answer 1

first principle?

Answer 2

i think you mean find it's derivative, since there is only one independent variable.

Answer 3

if it is derivative, then slope of the tangent= f'(x)=1/2 x^(-1/2)

Answer 4

he says using first princple

Answer 5

The question requires first principles

Answer 6

if you know binomial expansion it's quite easy

Answer 7

\[\lim_{h\to0}\frac{f(x+h)-f(x)}h\]This is first principle, right?\[\lim_{h\to 0}\frac{\sqrt{x+h} - \sqrt{x}}h\]Rationalize the Numerator.\[\lim_{h\to 0}\frac{\sqrt{x+h} - \sqrt{x}}h\times \frac{\sqrt{x+h} + \sqrt{x}}{\sqrt{x+h} +\sqrt{x}}\]And now some algebraic manipulation.

Answer 8

Oo ,,, i never imagined such method was still there.