use the function below to answer parts (a)-(c).\n$f(x)=x^{2}+2$\n(a) use the formal definition to find the…

use the function below to answer parts (a)-(c).\n$f(x)=x^{2}+2$\n(a) use the formal definition to find the derivative of $y = f(x)$ at $x = 1$.\n(b) find $f(1)$ and find the equation of the tangent line at the point $(1, f(1))$.\n(c) graph $y = f(x)$ and the tangent line at the point $(1, f(1))$ in the same coordinate system.\n(a) the derivative of a function $f$ at $x$, denoted by $f(x)$, is $f(x)=lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}$ provided that the limit exists. use the\nof the derivative of $f$ at $x$ to find the derivative of the given function $f(x)$ when $x = 1$.\n$$f^{prime}(1)=lim _{h \rightarrow 0} \frac{left(1+h)^{2}+2\right-left(1)^{2}+2\right}{h}$$\nevaluate the limit expression to find $f^{prime}(1)$.\n$f^{prime}(1)=2$ (type an integer or a fraction.)\n(b) $f(1)=\\square$ (type an integer or a fraction.)

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