What is the equation of the tangent line?

Question

Find an equation of the tangent line to the curve 𝑦 = 𝑥³ − 3𝑥² + 5𝑥 , 0 ≤ 𝑥 ≤ 3 that has the least slope.

This is little bit tricky for me but consider the first derivative of the function as the equation of the slope as a function of 𝑥 .Finding the point in the curve with the least slope means that one must take the derivative of the slope function and proceed as he/she would solve for critical the point(s).

Answer 1

The derivative represents the slope of the function at different values of x.

To find the least slope, take the derivative and find when f '(x) is the smallest

y' = 3x² + 6x + 5

If you graph this, you'll see that on the interval [0, 3], 5 is the smallest value for y', so 5 is the least slope

Do you think, you can solve for the equation of the tangent line?