1. The problem statement, all variables and given/known data
Find the gradient of the tangent at x on the following curve
##y=3x^2##
2. Relevant equations
$$\lim_{\Delta x\rightarrow 0}\frac{f(x+\Delta x)-f(x)}{\Delta x}$$
3. The attempt at a solution
I know that it's ##6x##.
$$\frac{3(x+\Delta x)^2-3x^2}{\Delta x}$$
$$=\frac{3x^2+6x\Delta x +3{\Delta x}^2-3x^2}{\Delta x}$$
$$=\frac{3\Delta x(2x + \Delta x)}{\Delta x}=2x+3\Delta x$$
$$\lim_{\Delta x\rightarrow 0}2x+3\Delta x =2x$$
:confused:
Where did I go wrong?
Find the gradient of the tangent at x on the following curve
##y=3x^2##
2. Relevant equations
$$\lim_{\Delta x\rightarrow 0}\frac{f(x+\Delta x)-f(x)}{\Delta x}$$
3. The attempt at a solution
I know that it's ##6x##.
$$\frac{3(x+\Delta x)^2-3x^2}{\Delta x}$$
$$=\frac{3x^2+6x\Delta x +3{\Delta x}^2-3x^2}{\Delta x}$$
$$=\frac{3\Delta x(2x + \Delta x)}{\Delta x}=2x+3\Delta x$$
$$\lim_{\Delta x\rightarrow 0}2x+3\Delta x =2x$$
:confused:
Where did I go wrong?
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