a curve is defined by y=2x^2 - 10x +7. point (3, -5) lies on this curve. find the equation of the normal to this curve
equation of tangent is y - y1 = m(x-x1). differentiating y gives us the value of m. so dy/dx = 4x-10. we know x is 3. therefore, dy/dx = m = 2 but we need equation of the normal, which is y-y1=(1/m)(x-x1). 1/m is 1/2. y1 = -5. x1 = 3 putting it all in gives us 2y = x - 13, and that is the equation of the normal to this curve.
HH
Related Maths A Level answers
All answers ▸The curve C has equation: 2x^2y + 2x + 4y – cos (piy) = 17. Use implicit differentiation to find dy/dx in terms of x and y.
Find the antiderivative of the function f(x)=cos(2x)+5.
Integrate(1+x)/((1-x^2)(2x+1)) with respect to x.
Find the first three terms in the expansion of (4-x)^(-1/2) in ascending powers of x.