Question

Pls help me with this calculus question

Answer 1

5

Explanation:

Gradient (slope) of the curve can be found by deriving a curve function.

In this scenario, the given function is a polynomial function which we can use Power Rules to derive it.

Power Rules

`\displaystyle{y=ax^n \to y' = nax^(n-1)}`

Thus, using the power rules, we will have:

`\displaystyle{y'=3x^2-4x+5}`

Note that deriving a constant will always result in 0.

Then the problem gives us that we want to find the slope or gradient at where the curve crosses y-axis.

The curve crosses y-axis at x = 0 only. Therefore, we substitute x = 0 in a derived function.

`\displaystyle{y'(0) = 3(0)^2-4(0)+5}\\\\\displaystyle{y'(0) = 5}`

Therefore, the slope at the point where a curve crosses y-axis will be 5.