at a particular point of the curve y = x 2 + k, the equation of the tangent is y = 6x - 7. find the value of the constant k .
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firstly find slop, the value of slop is 3, Now put x=3 in x^2+k=6x-7 K=2
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Answer:
k=2
Step-by-step explanation:
1)Equation of tangent is y=6x-7
from this equation you can find the gradient of tangent which is 6
2)Using differentiation to differentiate the equation of the curve,y=x²+k
dy/dx=2x
3)Equate both equation of curve and tangent:
x²+k=6x-7
x²-6x+k+7=0 and substitute x=3 into this equation.
Therefore k=2
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