Find the equation of the tangent to curve y=5x^2-2x+3 at the point x=0

y=5x2-2x+3 Differentiate to find the equation of the gradient of the curve
dy/dx=10x-2 Substitute x=0 to find the gradient at the point x=0
dy/dx=-2

y=50^2-20+3 Substitute x=0 into the original equation to find y at that point
y=3

y=mx+c Using y=mx+c and substituting x=0, y=3 and m=-2 to find c
3=-2*0+c
c=3 Substitute m=-2 and c=3 to find the equation of the tangent
y=-2x+3

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(1.) f(x)=x^3+3x^2-2x+15. (a.) find the differential of f(x) (b.) hence find the gradient of f(x) when x=6 (c.) is f(x) increasing or decreasing at this point?


a) Solve the following equation by completing the square: x^(2)+ 6x + 1= 0. b) Solve the following equation by factorisation: x^(2) - 4x - 5 = 0 c) Solve the following quadratic inequality: x^(2) - 4x - 5 < 0 (hint use your answer to part b)


The points P (2,3.6) and Q(2.2,2.4) lie on the curve y=f(x) . Use P and Q to estimate the gradient of the curve at the point where x=2 .


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