```python
from IPython.display import Image
from IPython.core.display import HTML 
from sympy import *
Image(url= "https://i.imgur.com/fP6ard7.png")
```









```python
L  = Function("L")
f = Function("f")
x,a = symbols('x a')
L(x)
```




$\displaystyle L{\left(x \right)}$




```python
Eq(L(x) , f(a) + diff(f(a),a)*(x-a))
```




$\displaystyle L{\left(x \right)} = \left(- a + x\right) \frac{d}{d a} f{\left(a \right)} + f{\left(a \right)}$




```python
Eq(f(x), x**Rational(3/4))
```




$\displaystyle f{\left(x \right)} = x^{\frac{3}{4}}$




```python
Eq(f(x), x**Rational(3/4)).subs(x,16)  
```




$\displaystyle f{\left(16 \right)} = 8$




```python
fa = 8        # f(a) = 8
f = lambdify(x, x**Rational(3/4), "math")
df = diff(f(x),x)
```


```python
Eq(Derivative(f(x)),df).subs(x,16)
```




$\displaystyle \left. \frac{d}{d x} x^{0.75} \right|_{\substack{ x=16 }} = 0.375$




```python
a = 16
dfa= df.subs(x,16)
Eq(L(x) , fa+ dfa*(x-a))
```




$\displaystyle L{\left(x \right)} = 0.375 x + 2.0$




```python
Image(url= "https://i.imgur.com/BesUBIc.png")
```








c9b8c981759e9f2e1b10fa35c0ec6c94aae24242
ipynb
Jupyter Notebook
Calculus_Homework/WWB15.1.ipynb
NSC9/Sample_of_Work
8f8160fbf0aa4fd514d4a5046668a194997aade6
MIT
Calculus_Homework/WWB15.1.ipynb
NSC9/Sample_of_Work
8f8160fbf0aa4fd514d4a5046668a194997aade6
MIT
Calculus_Homework/WWB15.1.ipynb
NSC9/Sample_of_Work
8f8160fbf0aa4fd514d4a5046668a194997aade6
MIT
Qwen/Qwen-72B
1. YES
2. YES