## Equation of a Tangent Line: Problems and Solutions

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Ferro Baltazar
2 months ago

Normal line to the curve y=2x² at a point in the first quadrant passed through the point (0,¾) ,find an equation of this normal line please show solution

Matheno
Editor
2 months ago

Hi, Ferro,

Thanks for asking! This is a good problem. We like it so much we added it as a sample problem #3 above.

We hope that helps! : )

Anonymous
9 months ago

Y=x5 at the point 1,5 give the solution

Matheno
Editor
9 months ago

(1) the given equation is y = 5x, in which case the function is a line and so is tangent to itself,

or

(2) the given equation is y = x^5, in which case the point (1,5) isn’t on the curve, but the point (1,1) is.

If you clarify which choice, if either, is the correct question, we’ll try to provide more detail about the solution.

Anonymous
1 year ago

Y=x³at the point 1,1 give the solution

Matheno
Editor
1. The slope of the tangent line at (1,1) equals the derivative at that point. Since $y=f(x)= x^3,$ the derivative is $y’=f'(x) =3x^2.$ Hence the slope of the tangent line at $x_0 = 1$ is $m_{tangent} = f'(1) = 3.$
2. Then we can write the equation of this tangent line, using the point-slope form of the line that has slope $m_{tangent} = 3$ and contains the point (1,1):
$$y – 1 = 3(x-1)$$