Looks difficult ??
Given the function f(x)= - 3 + 2x
Find the equation of the line that is tangent to the curve y=f(x) at point (a,f(a)). Take a look at the constant, hence find the coefficient of at the constant.
The answer is 3.
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1 solution
The equation of the tangent is y − f ( a ) = f ′ ( a ) ( x − a ) . We can calculate that f ′ ( x ) = 3 x 2 − 6 x . So the equation of the tangent line is y = ( 3 a 2 − 6 a ) ( x − a ) + ( a 3 − 3 a 2 + 2 a ) , or
y = ( 3 a 2 − 6 a ) x + ( − 2 a 3 + 3 a 2 + 2 a )