Answer:
5
Step-by-step 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
[tex]\displaystyle{y=ax^n \to y' = nax^{n-1}}[/tex]
Thus, using the power rules, we will have:
[tex]\displaystyle{y'=3x^2-4x+5}[/tex]
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.
[tex]\displaystyle{y'(0) = 3(0)^2-4(0)+5}\\\\\displaystyle{y'(0) = 5}[/tex]
Therefore, the slope at the point where a curve crosses y-axis will be 5.
