tangent line For what values of a and b is the line 4x+y=b t
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tangent line For what values of a and b is the line 4x+y=b tangent to the curve y=ax^3 when x=5?
求详细解答
求详细解答
Assume a and b are constants
4x+y=b
y=b-4x
gradient(m)=-4
y=ax³
dy/dx=3ax²
since line is tangent to curve,
3ax²=-4
when x=5,3a(5)²=-4
a=-4/75
y=(-4/75)(5)³
=-20/3
4x+y=b
4(5)+(-20/3)=b
b=40/3
4x+y=b
y=b-4x
gradient(m)=-4
y=ax³
dy/dx=3ax²
since line is tangent to curve,
3ax²=-4
when x=5,3a(5)²=-4
a=-4/75
y=(-4/75)(5)³
=-20/3
4x+y=b
4(5)+(-20/3)=b
b=40/3
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