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How do you find the value of c when the straight line y equals x plus c touches the curve y equals 3 -x -5x squared?
Wiki User
∙ 13y ago
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Dahlia Hagenes
Wiki User
∙ 13y agoThe gradient of the curve at any point on it = -1 -10x
The gradient of the line at any point on it = 1
The line and the curve touch where the two gradients are equal
ie -1 -10x = 1 or 10x = -2 or x = -0.2
When x = -0.2, the curve gives y = 3 + 0.2 - 5*0.04 = 3 + 0.2 - 0.2 = 3
So (x,y) = (-0.2, 3) is the point of contact between the curve and the line
Therefore these coordinates must satisfy the equation of the line
ie 3 = -0.2 + c so that c = 3.2
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