Question 1190587
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Part i)


Use the power rule to get the derivative
f(x) = x^2
f ' (x) = 2x


The derivative function will directly determine the slope of the tangent line.


If x = 1, then
f ' (x) = 2x
f ' (1) = 2*1
f ' (1) = 2
The slope of the tangent is m = 2 when x = 1.


Plug x = 1 into the original function
f(x) = x^2
f(1) = 1^2
f(1) = 1
The point (1,1) is on the f(x) curve.


Now apply the point-slope form
y - y1 = m(x - x1)
y - 1 = 2(x - 1)
y - 1 = 2x - 2
y = 2x-2+1
y = 2x-1


The slope of the tangent line is <font color=red>y = 2x-1</font> when x = 1


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For part ii), you'll follow very similar steps.


Use f ' (x) = 2x from earlier.


You should get a tangent slope of m = 8 and the point (4,16) is on the parabola.

 
The equation of the tangent line is <font color=red>y = 8x-16</font> when x = 4. 
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