Question

Please Help Me! I am giving you all my points to whoever answers this question because I don't know how to do this questions.

Using first principle, find the slope of a tangent line to the curve f(x) = x^2 - 3x +5 at x=3

Answer 1

y=3x−4

Explanation:

find the tangent line to f(x)=x2−3x+5 at x=3

First, find the value of the function at the given point: y0=f(3)=5

Second, find the slope of the tangent line, which is the derivative of the function, evaluated at the point: m=f′(3)

Find the derivative: f′(x)=2x−3

Next, we evaluate the derivative at the given point to find the slope.

m=f′(3)=3

Finally, the equation of the tangent line is y−y0=m(x−x0)

Plug the values that we found, we get that y−(5)=3(x−(3))

So basically: y=3x−4