Question
Let f(x) = x ^3. The equation of the tangent line to f(x) at x = 3 is
y= ?.
Using this, we find our approximation for 2.7 ^3 is
y= ?.
Using this, we find our approximation for 2.7 ^3 is
Answers
Damon
df(x)/dx = 3 x^2
that is the slope
at x = 3
slope = 3*9 = 27
so y = 27 x + b
put in point at x = 3 to find b
27 =27 * 3 + b
so
-54 = b
so
y = 27 x - 54
at x = 2.7
y = 27 * 2.7 -54 = 18.9
the real answer would be
y = 19.7
that is the slope
at x = 3
slope = 3*9 = 27
so y = 27 x + b
put in point at x = 3 to find b
27 =27 * 3 + b
so
-54 = b
so
y = 27 x - 54
at x = 2.7
y = 27 * 2.7 -54 = 18.9
the real answer would be
y = 19.7