48 Part I: The Questions
Finding All Points on a Graph
Where Tangent Lines Have a
Given Value
310–311 Find all points on the given function where
the slope of the tangent line equals the indicated
value.
310. Find all x values where the function
f
 
(x) = x
3
– x
2
– x + 1 has a horizontal
tangent line.
311. Find all x values where the function
f
 
(x) = 6x
3
+ 5x – 2 has a tangent line
with a slope equal to 6.
305. f x
x
x
( ) =
+
+
4
8
5
3 7
−
306. f x
x
x
x
x
( ) =
+
1 2
3
2
−





 (
)
307. f
 
(x) = (x
−3
+ 4)(x
−2
– 5x)
308. f
 
(x) = 4x
4
– x
2
+ 8x + π
2
309. f x
x
x
( ) =
− 1
4