Find an equation of the tangent line to the graph of y = f(x) at x = 2 if f(2) =

Question

Find an equation of the tangent line to the graph of y = f(x) at x = 2 if f(2) = -2 and f' (2) = -1. Find d^2 y/dx^2. Y = 7x^3 - 5x^2 + x y = 12x^2 - 2x + 3 y = x + 1/x y = (5x^2 - 3)(7x^3 + x) y = 4x^7 - 5x^3 + 2x y = 3x + 2 y = 3x - 2/5x y = (x^3 - 5)(2x + 3) Find y'". y = x^-5 + x^5 y = 1/x y = ax^3 + bx + c (a, b, c constant) y = 5x^2 - 4x + 7 y = 3x^-2 + 4x^-1 + x y = ax^4 + bx^2 + c (a, b, c constant) Find f'" (2), where f(x) = 3x^2 - 2 d^2 y/dx^2|_x=1, where y = 6x^5 - 4x^2 d^4/dx^4 [x^-3]|_x=1 Find y'" (0), where y = 4x^4 + 2x^3 + 3 d^4 y/dx^4|_x=1, where y = 6/x^4. Show that y = x^3 + 3x + 1 satisfies y'" + xy" - 2y' = 0. Show that if x notequalto 0, then y = 1/x satisfies the equation x^3 y" + x^2 y' - xy = 0.

Explanation / Answer

41)

a)given y =7x3-5x2+x

differentiate with respect to x , d/dx xn =nxn-1

dy/dx =7*3x2-5*2x+1

dy/dx =21x2-10x+1

differentiate with respect to x

d2y/dx2 =21*2x-10*1+0

d2y/dx2 =42x-10

b)

given y =12x2-2x+3

differentiate with respect to x , d/dx xn =nxn-1

dy/dx =12*2x-2*1+0

dy/dx =24x-2

differentiate with respect to x

d2y/dx2 =24*1 -0

d2y/dx2 =24

c)given y =(x+1)/x

y=(x/x)+(1/x)

y=1+x-1

differentiate with respect to x , d/dx xn =nxn-1

dy/dx =0+(-1)x-1-1

dy/dx =-x-2

differentiate with respect to x

d2y/dx2 =-(-2)x-2-1

d2y/dx2 =2x-3

d)y=(5x2-3)(7x3+x)

y=(35x5+5x3-21x3-3x)

y=35x5-16x3-3x

differentiate with respect to x , d/dx xn =nxn-1

dy/dx =35*5x4-16*3x2-3*1

dy/dx =175x4-48x2-3

differentiate with respect to x

d2y/dx2 =175*4x3-48*2x-0

d2y/dx2 =700x3-96x

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