Question
Question: The equation of tangent to the graph of the function f(x) = \|x<sup>2</sup> – \|x\|\| at the point ...
The equation of tangent to the graph of the function
f(x) = |x2 – |x|| at the point with abscissa x = –2 is
A
3x + y + 4 = 0
B
5x – y – 12 = 0
C
5x + y + 8 = 0
D
3x + y – 4 = 0
Answer
3x + y + 4 = 0
Explanation
Solution
f(x) = x2 + x at x = – 2
f ′(x) = 2x + 1
⇒ f ′(–2) = – 4 + 1 = – 3
f (–2) = 4 – 2 = 2
equation of tangent
y – 2 = – 3 (x + 2) ⇒ 3x + y + 4 = 0