If the tangent to the curve y-x3-ax-b at P-1-6- is parallel to the line y-x-5-find a-b

Y=x3+ax+b ...(1) y'= 3x2+a Slope of tangent at (1, 6)= 3(1)2+a=a+3 The slope of line y x=5 is ( 1)/1=1 So, a+3=1 a= 2 From (1), y=x3 2x+b It passes t ...

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Byju's Answer

Standard XII

Mathematics

Tangent of a Curve y =f(x)

if the tangen...

Question

if the tangent to the curve y=x³+ax+b at P(1,-6) is parallel to the line y-x=5,find a,b

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Solution

y=x³+ax+b ...(1)
y'= 3x²+a
Slope of tangent at (1,-6)= 3(1)²+a=a+3
The slope of line y-x=5 is -(-1)/1=1
So, a+3=1
a=-2

From (1),
y=x³-2x+b
It passes through P(1,-6)
-6=1-2+b
-6=-1+b
b=-5

So a=-2 and b=-5

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if the tangent to the curve y=x3+ax+b at P(1,-6) is parallel to the line y-x=5,find a,b

y=x3+ax+b ...(1) y'= 3x2+a Slope of tangent at (1,-6)= 3(1)2+a=a+3 The slope of line y-x=5 is -(-1)/1=1 So, a+3=1 a=-2 From (1), y=x3-2x+b It passes through P(1,-6) -6=1-2+b -6=-1+b b=-5 So a=-2 and b=-5

if the tangent to the curve y=x³+ax+b at P(1,-6) is parallel to the line y-x=5,find a,b

y=x³+ax+b ...(1)
y'= 3x²+a
Slope of tangent at (1,-6)= 3(1)²+a=a+3
The slope of line y-x=5 is -(-1)/1=1
So, a+3=1
a=-2

From (1),
y=x³-2x+b
It passes through P(1,-6)
-6=1-2+b
-6=-1+b
b=-5

So a=-2 and b=-5