Answer:
gradient = 9
Step-by-step explanation:
The gradient of the tangent at x = a is the derivative [tex]\frac{dy}{dx}[/tex]
Differentiate using the power rule on each term
[tex]\frac{d}{dx}[/tex] (a[tex]x^{n}[/tex] ) = na[tex]x^{n-1}[/tex] and [tex]\frac{d}{dx}[/tex] ( constant ) = 0
y = 2x² + 5x - 3
[tex]\frac{dy}{dx}[/tex] = 2.2[tex]x^{2-1}[/tex] + 5[tex]x^{1-1}[/tex] - 0
= 4x + 5
[tex]\frac{dy}{dx}[/tex] ( x = 1 ) = 4(1) + 5 = 4 + 5 = 9 ← gradient of tangent
