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Pls help me with this calculus question

Pls help me with this calculus question-example-1
User Norrin Rad
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1 Answer

1 vote

Answer:

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.

User Adrianwadey
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