Let
f(x) = 2x^2 - 3 if x <= 2
gx) = ax - 7 if x > 2
Find a if the graph of y = f(x) is continuous
Hello Guest!
\(\color{BrickRed}f(x)=2x^2-3\\ \color{blue}f'(x)=4x=a\\ \color{BrickRed}g(x)=ax-7\\ 4x = a\ inserted\ in\ g (x)\\ g(x)=4x^2-7\\ \color{blue} f(x)=g(x)\)
\(2x^2-3=4x^2-7\\ 2x^2=4\\ \color{blue}x=\pm \sqrt{2}\)
\(y=2\cdot 2-3\)
\(y=1\)
\(g(x)=ax-7\\ 1=a\cdot \sqrt{2}-7\\ a=4\cdot \sqrt{2}\)
\(a=5.65685\\ g(x)=5.65685x-7\)
\(y\in \{f(x)=2x^2-3\}\ |-∞ LaTeX is crazy today!
y \(\in\) {f(x)=\(2x^2\)-3} | (\(-∞\) < x \(\le \sqrt{2}\) )
y \(\in\) {g(x)=5.65685y-7} | (\(\sqrt{2}\) < x \( \le 2\))
y \(\in\) {g(x)=5.65685x-7} | (\(2\) < x < \(∞\))
!
+2236 
