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# FSMQ Differentitaion Questions

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1. Equation of graph is - y=x^3+x^2-5x-2
1. Show that there is a turning point when x=1 and find the x co-ordinate of the turning point
2.Find the equation of the tangent at the point (0,-2)
3.Find the equation of the normal at the point (2,0)
Thanks
2. (Original post by Sandrathomas)
Equation of graph is - y=x^3+x^2-5x-2
1. Show that there is a turning point when x=1 and find the x co-ordinate of the turning point
2.Find the equation of the tangent at the point (0,-2)
3.Find the equation of the normal at the point (2,0)
Thanks
1. Differentiate the function to get 3x^2 + 2x -5, then equate it to zero and solve teh quadratic , which should give you 2 turning points , one being x =1.

2. sub in x= 0 into 3x^2 +2x- 5 , you get -5 , so the gradient of the tangent is -5, therefore y= -5x + c, sub in your coordiante (0, -2) to find C and that is your equation.

3. the gradient of the normal is the negative reciprocal of the gradient of the tangent , which is 1/5 so y= 1/5x+c , sub in (2,0) to find your equation.
3. (Original post by ihatehannah)
1. Differentiate the function to get 3x^2 + 2x -5, then equate it to zero and solve teh quadratic , which should give you 2 turning points , one being x =1.

2. sub in x= 0 into 3x^2 +2x- 5 , you get -5 , so the gradient of the tangent is -5, therefore y= -5x + c, sub in your coordiante (0, -2) to find C and that is your equation.

3. the gradient of the normal is the negative reciprocal of the gradient of the tangent , which is 1/5 so y= 1/5x+c , sub in (2,0) to find your equation.
Thankyou so much, this really helped x
4. (Original post by Sandrathomas)
Thankyou so much, this really helped x

Heya, can I just check something?
1. x is 1 or -5/3, so is is -5/3 the answer?
2. y=-5x-2?
3. y=1/5x+-2/5?
5. (Original post by Sandrathomas)
Heya, can I just check something?
1. x is 1 or -5/3, so is is -5/3 the answer?
2. y=-5x-2?
3. y=1/5x+-2/5?
yeah thats right

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