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Find the linearization $L(x)$ of the function at $a$$$f(x)=x^{3 / 4}, \quad a=16$$
$L(x)=\frac{3}{8} x+2$
Calculus 1 / AB
Chapter 2
DERIVATIVES
Section 8
Linear Approximations and Differentials
Derivatives
Differentiation
Applications of the Derivative
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So in this question, we want to find out of miniaturization a taxi cost way, which is just attention line. So by the slump point form for attention line. We have to figure out these three information. So the sooner point from give is given by White minus a full face because toe prime of eight, which is a motive and it's a stroke off attention line Times X minus eight So a is given a 16. So we need to figure out what safe off a and they've profit. So if a way equals two f off off 16 which is, um, 16 23 over full, I'm so be careful about this. It's actually close to 16 to the 1/4 ended to the three. So you inside the break it and we have just two so immune evaporate en route for duty. If we need to figure out the curative off first, I love power or it's given by three or four extreme minus 1/4, and we plug in X equals 2 16 So we have 3/4, um, comes one over 16 to the one number fault. So we just given by 3/8 With this information, we have wide miners hit because 23 or rate times X service 16 Some of this mind state to the other side we have Why? Because toe through over eight ex miners the second Article six in the process which is through your rate takes pass to so the immunization is given by this through over eight express to
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