Find value of if tangent to the curve y=x2-ax+7 is parallel to line
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Answer:
a=−4,b=7→y=x2−4x+7
Explanation:
y=x2+ax+b
y'=2x+a
We are told that the tangent at x=1 is 2x+y=6
→y=−2x+6
Therefore the slope of the tangent =−2
Since the slope of y at x=1 is given by y'(1)
2(1)+a=−2
a=−4
Now notice that y(1)=12+(−4)⋅1+b
y(1)=−3+b
Since the tangent touches y at x=1
y(1)=−2(1)+6→y(1)=4
Therefore: −3+b=4→b=7
Hence: a=−4,b=7
y=x2−4x+7
a=−4,b=7→y=x2−4x+7
Explanation:
y=x2+ax+b
y'=2x+a
We are told that the tangent at x=1 is 2x+y=6
→y=−2x+6
Therefore the slope of the tangent =−2
Since the slope of y at x=1 is given by y'(1)
2(1)+a=−2
a=−4
Now notice that y(1)=12+(−4)⋅1+b
y(1)=−3+b
Since the tangent touches y at x=1
y(1)=−2(1)+6→y(1)=4
Therefore: −3+b=4→b=7
Hence: a=−4,b=7
y=x2−4x+7
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